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The cricket system, as a strongly coupled, nonlinear and multivariable two dimensional cue system, is a typical representative of unstable and underactuated system. In this paper, the system is analyzed by modeling based on the cricket experimental platform, and while designing the LQR controller, the particle swarm algorithm is introduced to optimize the controller parameters to determine the optimal weight matrix Q in order to solve the difficult problem of controller parameter rectification. The simulation results show that the PSO-LQR can restore the balance of the system in a shorter period of time with enhanced stability compared to a single LQR controller, which exhibits good control performance.

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Isolating causal genes from enormous genome-wide association signals of complex phenotypes remains an open and challenging question. SMR (Summary-based Mendelian Randomization) is a widely used Mendelian randomization (MR) method for inferring causal genes by using a single expression quantitative trait locus (eQTL). In the present study, we explored more powerful MR methods based on multiple eQTLs. Among six representative multiple instrumental variable (IVs) based MR methods, original used in the epidemiological field, not all MR methods worked for the causal gene estimation. But we found the maximum-likelihood based MR method and weighted median-based MR method were preferable to the other four MR methods in terms of valid type 1 errors, acceptable statistical powers and robustness to linkage disequilibrium (LD) in eQTLs. Both of the MR methods were also much more powerful than the SMR. We recalibrated key parameters of the two MR methods in practices and developed a multiple IVs based MR analysis framework for causal gene estimation, named MACG and available at http://pmglab.top/kggsee. In the applications, MACG not only rediscovered many known causal genes of the schizophrenia and bipolar disorder, but also reported plenty of promising candidate causal genes. In conclusion, this study provided a powerful tool and encouraging exemplars of mining potential causal genes from huge amounts of GWAS signals with eQTLs.